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From: brad@huey.Jpl.Nasa.GOV (Brad Hines)
Newsgroups: comp.music,rec.music.synth
Subject: Re: Looking for Equations for Sounds
Message-ID: <10981@jpl-devvax.JPL.NASA.GOV>
Date: 10 Jan 91 05:15:24 GMT
References: <278a4f64.4051@petunia.CalPoly.EDU>
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In article <278a4f64.4051@petunia.CalPoly.EDU>, sseidman@polyslo.CalPoly.EDU (The MIDIman) writes:
|> 
|> 
|> For my Senior Project, I am writing a simple type of Additive Synthesis
|> program, which will transfer the sound created to a sampler.  It will
|> be Additive Synthesis, but with some FM capabilities.  Basically, the
|> user creates carriers, and then can create modulators which feed into the
|> carriers.
|> 
|> My problem is finding the shape of the sound/graph.  For JUST carriers, I
|> would think I could just add up all the Sine equations, and this would
|> give me the point on the graph at a point.  But I am not sure how to
|> find the equation when I start adding in modulators.  Would it be something
|> like: Sin (Sin X) X + Sin (Sin X) X, with the Sin X in prantheses being the
|> modulator?  Does anyone have any references of books to look at?
|> 
|> Thanks for any help.


Your basic sine:

	f(t) = A * sin ( 2*pi*f*t + phi_0 )

A is the amplitude of the sine wave
f is the frequency of the wave
phi_0 is an arbitrary phase offset

As there are three parameters, A, f, and phi_0, there are three
kinds of modulation you can do: Amplitude Modulation, Frequency
Modulation, and Phase Modulation.

AM is Amplitude Modulation, so you modulate A:

	f(t) = ( A_0 + dA(t) ) * sin ( 2*pi*f*t + phi_0 )

A_0 is the amplitude of the carrier
dA(t) is the modulation function

FM is Frequency Modulation, so you modulate f:

	f(t) = A * sin ( 2*pi*( f_0 + df(t) )*t + phi_0 )

f_0 is the carrier frequency
df(t) is the modulation function

PM is Phase Modulation (not so common as the other two):

	f(t) = A * sin ( 2*pi*f*t + ( phi_0 + dphi(t) ) )

phi_0 is the phase offset of the wave
dphi(t) is the modulation function


-- 
Brad Hines
Internet: brad@huey.jpl.nasa.gov

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